The [Lagrangian for electromagnetic waves][1] shows that its energy has a kinetic part as well as a potential part (just like everything else). The potential part only exists in a medium whereas in the vacuum all energy in electromagnetic waves are kinetic. 

Similar formulation exists for mechanical (e.g. elastic) waves. In this case, I understand easily that the kinetic energy is simply the intensity of shaking/amplitude of waves (e.g. in an earthquake) whereas the potential energy is the so-called strain energy which is basically just the potential energy associated for a spring.

Returning back to electromagnetic waves, I can understand that the kinetic energy is, again, the amplitude of the waves that is manifested by e.g. light brightness or heat (which originates from the motion/collision of particles). However, I am having a hard time thinking of an intuitive interpretation for potential energy for electromagnetic waves. I only know that this only exists in non-vaccum space. So, what is the potential energy for all the electromagnetic waves we create here on earth, which are traveling in the air that is non-vaccum. Are there examples of familiar electromagnetic waves that does not have (or have very little) kinetic energy but is purely all potential energy? 


  [1]: https://quantummechanics.ucsd.edu/ph130a/130_notes/node452.html